Once you clear all of the clubs, Universe Tower will unlock. There's five dance battles that you have to clear inside, and they all have to be completed in succession. Meaning that if you leave before beating all five, you'll start over with the first one when you return.

Some of the battles are pretty rough. I recommend taking a backup dancer with you. Backup dancers can be obtained by beating most club challenges a second time. I recommend looking to challenge Lee in the middle ring of clubs. He can be found at Club Caelum. His challenge is pretty easy.